I have to disagree with your interpretation of 49 C.F.R. §1540.105(a)(2)
my qualms being in that it was not as strictly constructed as you seem to believe, as it did not limit the control of access to "screening" (limited to searching for WEI) exclusively...

Also 1540.107(c) would seem to be an enforcing clause to the requirements set forth in § 1560.105
yes, the operator does the watchlist matching, but the subsequent application of security procedures is contingent on the results of said matching; the transmission of this information being primarily in the form of boarding passes. So I guess they're counting reading the output as an extension of the matching process..

just a few thoughts... but then again, I'm barred having those by my management and the public... maybe if you could find a way to get TSA to follow the rule of law in really ANY case, all of us would be better off.